Taufeeq was not out on 39 and Hafeez was not out on 15, indulging themselves, hitting 11 boundaries between them, after the Pakistanis, looking for a series-levelling victory, dismissed West Indies for 223 about 1 ¼ hours before the interval to grab a first innings lead of 49.
In between an attractive array of strokes, the two openers gained two reprieves apiece however, helping to engineer a bright start to the visitors' second innings.
Hafeez was nought, when he edged the fourth ball of the innings - a no-ball - and was caught behind off Kemar Roach, and on 14, West Indies captain Darren Sammy spilled a second low chance at second slip off Ravi Rampaul.
Taufeeq was one in the third over, when he edged Roach to first slip, where Darren Bravo muffed a straightforward chance, and on 13, edged the same bowler to second slip, where Sammy put him down.
The two openers made the most of their opportunities however, with Taufeeq getting into his stride, when he added insult to injury, punching a delivery in Roach's second over through mid-on for his first boundary.
Hafeez got off the mark in the following over, when he pulled a short, rising delivery from Rampaul through mid-wicket.
Taufeeq followed up with two cracking off-side boundaries - a searing square cut through point, and a fluent drive through mid-off - in Roach's third over, which ended with a well-timed off-drive for four by Hafeez.
Taufeeq continued to rub salt into Roach's wounds in the fast bowler's fourth over, when he drove the fast bowler through mid-off, straight, and square for three more fours.
Hafeez also on-drove Rampaul for his third four, and Taufeeq greeted Sammy's medium-pace with a ferocious off-drive for his seventh boundary.
After a period of attrition, Taufeeq drove Rampaul straight for his eighth four, as West Indies suffered a setback, when Sammy pulled up with a sore back, leaving the field after completing his third over.
Earlier, Pakistan were frustrated, as West Indies, starting the day on 184 for eight, put up some resistance thanks to their tail-enders.
Hafeez made the breakthrough however, when he trapped Roach lbw playing back and across for a career-best 29, following a valuable 60-run stand for the ninth wicket with Rampaul.
Saeed Ajmal, Pakistan's most penetrative bowler in the brief series, brought the innings to a close, when Devendra Bishoo edged a forward defensive shot, and was caught at slip for one.
Hafeez was the pick of the Pakistani bowlers, finishing with a career-best three for 23 from eight overs, fellow off-spinner Ajmal ended with three for 56 off 28.5 overs, and left-arm spinner Abdur Rehman captured two for 55 from 29 overs.
The visitors trail 0-1 in the two-Test series, following a 40-run defeat inside four days in the first Test, which ended last Sunday at the Guyana National Stadium, crushing their dreams of a maiden Test series victory in the Caribbean.
Copyright AFP (Agence France-Presse), 2011